Heat oil over medium heat. Add the shallot or onion and ginger and cook gently until softened.
Add garlic and tomatoes. Simmer until the mixture begins to thicken. Add broth and milk and bring to a boil. Remove immediately from heat.
Transfer to a food processor or blender or use an immersion blender. Process until smooth. Return to pan and gently reheat. Serve immediate. Add salt and pepper to taste and garnish with chives or scallion.